I have been given the question:
I travel to work via route J or K. The probability that I chose route J is $\frac{1}{4}$. The probability that I am late for work if I chose route J is $\frac{2}{3}$. The corresponding probability if I go via route K is $\frac{1}{3}$.
Would the probability of me being late if I chose route J translate to: $P(Late|J)$ or $P(Late \land J)$
The probability that you are late if you choose route $J$ can be phrased as the probability you are late, given that you choose $J$, which is the word version of the expression $$P(\text{late} \mid J)$$
The probability that you are late and you choose route $J$ is a different concept, and is written $$P(\text{late} \wedge J)$$
The two expressions relate as follows:
$$P(\text{late} \mid J) \cdot P(J) = P(\text{late} \wedge J)$$
LaTeX tip: you can use \text{ } within math mode to display everything within the brackets as text instead of math.